Methodology: a conditional cash-notional capacity worksheet

The supported question and unit convention

Version capacity-scenarios/1.0.0 evaluates a static cash-notional basket. Supply capital in dollars and sleeve weights summing to one, including untraded cash where appropriate. Each row's traded fraction is the absolute portion of that sleeve traded during this window, from zero to one. The calculation is unsigned: it does not infer purchases, sales, target holdings, financing or netting between orders.

Dollar ADV means a per-session average dollar turnover assumption in the same currency as capital. Multiply it by the selected number of sessions and a common volume multiplier to obtain the window-volume assumption. A fractional session is a proportional-volume approximation, not an intraday volume forecast. Mixing currencies, shares and dollars, or futures margin and notional, produces a different and unsupported calculation.

Forward calculation

For row i, let C be capital, w its weight, t its traded fraction, D its dollar ADV, m the volume multiplier and H the session window. Order Q = C × w × t. Window volume V = D × m × H. Participation p = Q ÷ V for a positive order. Zero-order rows have zero trading cost and impose no boundary; a positive order requires positive dollar ADV.

Cost in basis points per traded dollar is c = fee + half spread + k × square root of p, where k is an illustrative impact coefficient. Dollar cost is Q × c ÷ 10,000. Add row costs to obtain basket cost. Divide by total traded notional for weighted execution-cost basis points, or by C for portfolio-drag basis points, multiplying either ratio by 10,000. These denominators answer different questions.

Invert the two selected constraints

Every traded row must satisfy both p ≤ participation cap and c ≤ cost budget. For positive k and a budget at least as large as fee plus half spread, cost-implied participation is ((budget − fee − half spread) ÷ k) squared. The effective participation allowance is the smaller of that value and the explicit cap. Each positive traded-weight row's capital boundary is allowance × V ÷ (w × t); the basket boundary is the smallest row boundary.

A budget below the fixed component permits no positive trade. If k is positive, a budget equal to that component also implies a zero capital boundary. If k is zero and the budget covers the fixed component, only the participation cap binds. An all-zero-order basket has undefined trading capacity. The interface should display that absence of a constraint, rather than an economically meaningful infinity.

What the cost curve does and does not represent

The default coefficient, fee, spread and volumes are invented demonstration values. They are not fitted market estimates. Research by Zarinelli and co-authors finds important limits to a square-root description, while Durin and co-authors examine separate volume and participation effects. Those papers motivate caution about functional form; neither establishes this calculator's parameters or validates the calculator for a particular instrument.

This implementation has no volatility factor, transient-impact path, order-book simulation, queue position, cross-impact, trading direction, market drift, alpha decay, opportunity cost or probability of completion. It does not incorporate borrow availability, dealer limits, derivative multipliers, margin, ownership limits or cash-flow obligations. Participation above 100% exposes an infeasible volume requirement; a finite extrapolated cost is not evidence that the order can execute.

Reproduction and decision use

The four worked cases retain independent forward and inverse calculations. Their underlying inputs are synthetic; their publication date is not a market observation date. JSON inputs preserve scenario assumptions and CSV reports preserve the engine version, units and output denominators. Keep unrounded calculations for reconciliation and round only the presentation.

Before applying this structure to real orders, establish lawful volume data, eligible venues and sessions, an appropriate cost calibration and the execution objective. Check a range of capital, volume, timing and cost assumptions. A boundary from one frozen scenario remains conditional on all of those inputs. It is neither a forecast of sustainable returns nor a recommendation to trade at the displayed maximum.

Keep in the decision record

• Use a single dollar currency and explicit session-volume assumptions.
• The minimum row boundary controls the basket.
• All default numerical inputs are illustrative; empirical calibration is a separate task.

Source notes

1. Zarinelli et al.: Beyond the square root
2. Durin, Rosenbaum and Szymanski: The two square root laws of market impact

Sources inform the definitions and limitations. Scenario inputs and arithmetic are publication illustrations, not extracted market observations. Access checks are dated in the source inventory.